x²+x>1. I can not remmeber how to solve this it doesnt make sense to me how you can have a single x and a negative 1. x(x+1)-1 ???

(Take a look at the graph I have attached.)

We are looking for the portion of the x-axis where the graph is above the x-axis.

We do this algebraically by the following process.

Solve according to the quadratic formula.

Now break the x-axis into three parts:

We want to test the inequality on each of these intervals. The idea is to pick the easiest number in the interval to do the test on, so for example pick -100000000000000 in the first interval, pick 0 in the second, and pick 100000000000000 in the last interval. (Or any other numbers you like.): Check!